A simplified model assumes that each nucleon interacts only with other nucleons lying inside a sphere of radius r0=2.0fm centred on it. The nuclear matter density may be taken as ρ=0.17nucleonsfm−3.
(a) For a nucleus whose radius is R=6.0fm, estimate the average number of neighbouring nucleons that a typical nucleon can interact with under this model.
(b) If the average interaction energy per interacting pair is ε=2MeV, estimate the binding energy per nucleon Ebn for this nucleus. Compare the value obtained with the typical experimental value of 8MeV and comment on the adequacy of the simplified model.